The sum of two angles is $78^\circ$. Angle 2 is $66^\circ$ smaller than $2$ times angle 1. What are the measures of the two angles in degrees?
Answer: Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 78}$ ${y = 2x-66}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${2x-66}$ for $y$ in the first equation. ${x + }{(2x-66)}{= 78}$ Simplify and solve for $x$ $ x+2x - 66 = 78 $ $ 3x-66 = 78 $ $ 3x = 144 $ $ x = \dfrac{144}{3} $ ${x = 48}$ Now that you know ${x = 48}$ , plug it back into $ {y = 2x-66}$ to find $y$ ${y = 2}{(48)}{ - 66}$ $y = 96 - 66$ ${y = 30}$ You can also plug ${x = 48}$ into $ {x+y = 78}$ and get the same answer for $y$ ${(48)}{ + y = 78}$ ${y = 30}$ The measure of angle 1 is $48^\circ$ and the measure of angle 2 is $30^\circ$.